Skip to main content

Part of the book series: Springer Handbooks ((SHB))

Abstract

Analogue models are actual physical setups used to model something else. They are especially useful when what we wish to investigate is difficult to observe or experiment upon due to size or distance in space or time; for example, if the thing we wish to investigate is too large, too far away, takes place on a time scale that is too long, does not yet exist or has ceased to exist. The range and variety of analogue models is too extensive to attempt a survey. In this chapter, I describe and discuss several different analogue model experiments, the results of those model experiments, and the basis for constructing them and interpreting their results. Examples of analogue models for surface waves in lakes, for earthquakes and volcanoes in geophysics, and for black holes in general relativity, are described, with a focus on examining the bases for claims that these analogues are appropriate analogues of what they are used to investigate. A table showing three different kinds of bases for reasoning using analogue models is provided. Finally, it is shown how the examples in this chapter counter three common misconceptions about the use of analogue models in physics.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 269.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 349.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Abbreviations

ABC:

amoeba-based computing

References

  1. W.W.G.J. Swoboda: The Thought and Work of the Young Ernst Mach and the Antecedents to His Philosophy, Ph.D. Thesis (Univ. Pittsburgh, Pittsburgh 1973)

    Google Scholar 

  2. J.T. Blackmore: Ernst Mach: His Work, Life, and Influence (Univ. California Press, Berkeley 1972)

    Google Scholar 

  3. S.G. Sterrett: Sounds like light: Einstein’s special theory of relativity and Mach’s work in acoustics and aerodynamics, Stud. Hist. Philos. Mod. Phys. 29, 1–35 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  4. P.A. Cherenkov: Nobel Lecture: Radiation of Particles Moving at a Velocity Exceeding That of Light, and Some of the Possibilities for Their Use in Experimental Physics, http://www.nobelprize.org/nobel_prizes/physics/laureates/1958/cerenkov-lecture.html (2014) Nobel Media AB 2014. Web. 2015

  5. C. Barcelo, S. Liberati, M. Visser: Analogue gravity, Living Rev. Relativ. 14(3), 1–179 (2011)

    MATH  Google Scholar 

  6. M. Visser, C. Barcelo, S. Liberati: Analogue models of and for gravity, Gen. Relativ. Gravit. 34(10), 1719–1734 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  7. D. Faccio: Laser pulse analogues for gravity and analogue Hawking radiation, Contemp. Phys. 53(2), 97–112 (2012)

    Article  Google Scholar 

  8. D. Faccio, F. Belgiorno, S. Cacciatori, V. Gorini, S. Liberati, U. Moschella (Eds.): Analogue Gravity Phenomenology: Analogue Spacetimes and Horizons from Theory to Experiment (Springer, Cham 2013)

    MATH  Google Scholar 

  9. M. Visser: Survey of analogue spacetimes. In: Analogue Gravity Phenomenology: Analogue Spacetimes and Horizons from Theory to Experiment, ed. by D. Faccio, F. Belgiorno, S. Cacciatori, V. Gorini, S. Liberati, U. Moschella (Springer, Cham 2013) pp. 31–50

    Chapter  Google Scholar 

  10. I. Carusotto, G. Rousseaux: The Cerenkov effect revisited: From swimming ducks to zero modes in gravitational analogues. In: Analogue Gravity Phenomenology: Analogue Spacetimes and Horizons from Theory to Experiment, ed. by D. Faccio, F. Belgiorno, S. Cacciatori, V. Gorini, S. Liberati, U. Moschella (Springer, Cham 2013) pp. 109–144

    Chapter  Google Scholar 

  11. B. Ayres: Mechanical models of the electric circuit, Electr. World 28, 276–277 (1896)

    Google Scholar 

  12. C.F. Jenkin: A dynamic model of tuned electrical circuits, Proc. Inst. Electr. Eng. 60, 939–941 (1922)

    Google Scholar 

  13. J.S. Small: The Analogue Alternative: The Electronic Analogue Computer in Britain and the USA, 1930–1975 (Routledge, New York, London 2001)

    Google Scholar 

  14. V. Bush, S.H. Caldwell: A new type of differential analyzer, J. Frankl. Inst. 240(4), 255–325 (1945)

    Article  MathSciNet  MATH  Google Scholar 

  15. A.G. MacNee: An Electronic Differential Analyzer, Technical Report No. 90, Research Laboratory of Electronics (MIT Press, Cambridge 1948)

    Google Scholar 

  16. B. Randell (Ed.): The Origins of Digital Computers: Selected Papers, Springer Monographs in Computer Science (Springer, Berlin, Heidelberg 1982)

    MATH  Google Scholar 

  17. C. Isenberg: The soap film: An analogue computer, Am. Sci. 64, 514–518 (1976)

    Google Scholar 

  18. M. Aono, Y. Hirata, M. Hara, K. Aihara: Combinatorial optimization by ameoba-based neurocomputer with chaotic dynamics. In: Natural Computing, Vol. 1, ed. by Y. Suzuki, M. Hagiya, H. Umeo, A. Adamatzky (Springer, Tokyo 2009) pp. 1–15

    Chapter  Google Scholar 

  19. E. Buckingham: Physically similar systems: Illustrations of the use of dimensional equations, Phys. Rev. 4, 345–376 (1914)

    Article  Google Scholar 

  20. H.L. Langhaar: Dimensional Analysis and Theory of Models (Wiley, New York 1951)

    MATH  Google Scholar 

  21. R.C. Pankhurst: Dimensional Analysis and Scale Factors (Chapman Hall, New York 1964)

    Google Scholar 

  22. S.L. Lien, J.A. Hoopes: Wind-driven, steady flows in Lake Superior, Limnol. Oceanogr. 23, 91–103 (1978)

    Article  Google Scholar 

  23. N.P. Wallerstein, C.V. Alonso, S.J. Bennett, C.R. Thorne: Distorted Froude-scaled flume analysis of large woody debris, Earth Surf. Process. Landf. 26, 1265–1283 (2001)

    Article  Google Scholar 

  24. S. De Rosa, F. Franco, V. Meruane: Similitudes for the structural response of flexural plates, Proc. Institution Mech. Eng, J. Mech. Eng. Sci. (2015), doi:10.1177/0954406215572436

  25. R. Frigg, S. Hartmann: Models in science. In: The Stanford Encyclopedia of Philosophy, ed. by E.N. Zalta http://plato.stanford.edu/archives/fall2012/entries/models-science/ (Fall 2012 Edition)

  26. R.N. Giere: Science Without Laws (Univ. Chicago Press, Chicago 1999)

    Google Scholar 

  27. R.N. Giere: How models are used to represent reality, Philos. Sci. 71, 742–752 (2004)

    Article  Google Scholar 

  28. G. Francesco: Models, simulations, and experiments. In: Model-Based Reasoning: Science, Technology, Values, ed. by L. Magnani, N. Nersessian (Kluwer, New York 2002) pp. 59–74

    Google Scholar 

  29. E. Winsberg: A tale of two methods, Synthese 169(3), 575–592 (2009)

    Article  Google Scholar 

  30. D. Rothbart (Ed.): Modeling: Gateway to the Unknown: A Work by Rom Harre (Elsevier Science, Amsterdam 2004), (Studies in Multidisciplinarity)

    Google Scholar 

  31. P. Kroes: Structural analogies between physical systems, Br. J. Philos. Sci. 40(2), 145–154 (1989)

    Article  Google Scholar 

  32. E.T. Layton: Escape from the jail of shape: Dimensionality and engineering science. In: Technological Development and Science in the Industrial Age: New Perspectives on the Science-Technology Relationship, ed. by P. Kroes, M. Bakker (Kluwer, Dordrecht, Boston 1992)

    Google Scholar 

  33. S.G. Sterrett: Dimensional analysis and similarity. In: Philosophy of Technology and Engineering Sciences, Vol. 9, ed. by A.W.M. Meijers (Elsevier, Amsterdam 2009) pp. 799–823

    Chapter  Google Scholar 

  34. S.G. Sterrett: Wittgenstein Flies a Kite: A Story of Models of Wings and Models of the World (Penguin, New York 2005)

    Google Scholar 

  35. S.G. Sterrett: Physical models and fundamental laws: Using one piece of the world to tell about another, Mind Soc. 5(3), 51–66 (2002)

    Article  Google Scholar 

  36. J. Mattingly, W. Warwick: Projectible predicates in analogue and simulated systems, Synthese 169, 465–483 (2009)

    Article  Google Scholar 

  37. S.D. Zwart: Scale modelling in engineering: Froude’s case. In: Philosophy of Technology and Engineering Sciences, Vol. 9, ed. by A.W.M. Meijers (Elsevier, Amsterdam 2009) pp. 759–798

    Chapter  Google Scholar 

  38. N. Oreskes: From scaling to simulation: Changing meanings and ambitions of models in geology. In: Science Without Laws, ed. by A.N.H. Creager, E. Lunbeck, M. Norton Wise (Duke Univ. Press, Durham, London 2007)

    Google Scholar 

  39. M.K. Hubbert: Theory of scale models as applied to the study of geologic structures, Geol. Soc. Am. Bull. 48, 1459–1520 (1937)

    Article  Google Scholar 

  40. M.K. Hubbert: Strength of the earth, Bull. Am. Assoc. Petroleum Geol. 29, 1630–1653 (1945)

    Google Scholar 

  41. O. Merle, A. Borgia: Scaled experiments of volcanic spreading, J. Geophys. Res. Solid Earth 101, 13805–13817 (1996)

    Article  Google Scholar 

  42. G. Norini, V. Acocella: Analogue modeling of flank instability at Mount Etna: Understanding the driving factors, J. Geophys. Res. (2011), doi:10.1029/2011JB008216

  43. V. Gabuchian, A.J. Rosakis, N. Lapusta, D.D. Oglesby: Experimental investigation of strong ground motion due to thrust fault earthquakes, J. Geophys. Res. Solid Earth 119, 1316–1336 (2014)

    Article  Google Scholar 

  44. J.N. Brune: Particle motions in a physical model of shallow angle thrust faulting, Proc. Indian Acad. Sci. 105, 197–206 (1996)

    Google Scholar 

  45. H. von Helmholtz: On discontinuous motions in liquids. In: Mechanics of the Earth’s Atmosphere: A Collection of Translations, Smithsonian Miscellaneous Collections, Vol. 843, ed. by C. Abbe (The Smithsonian Inst., Washington DC 1891) pp. 58–66

    Google Scholar 

  46. H. von Helmholtz: On a theorem relative to movements that are geometrically similar in fluid bodies, together with an application to the problem of steering balloons. In: Mechanics of the Earth’s Atmosphere: A Collection of Translations, Smithsonian Miscellaneous Collections, Vol. 843, ed. by C. Abbe (The Smithsonian Inst., Washington DC 1891) pp. 67–77

    Google Scholar 

  47. W.G. Unruh: Experimental black-hole evaporation?, Phys. Rev. Lett. 46, 1351–1353 (1981)

    Article  Google Scholar 

  48. R. Courant, K.O. Friedrichs: Supersonic Flow and Shock Waves (Springer, New York 2012), reprint of original 1948 edition

    MATH  Google Scholar 

  49. A. Bramati, M. Modugno (Eds.): Physics of Quantum Fluids: New Trends and Hot Topics in Atomic and Polariton Condensates (Springer, Heidelberg 2013)

    Google Scholar 

  50. M. Born: Einstein’s Theory of Relativity (Dover, New York 1962)

    Google Scholar 

  51. R. Schutzhold, W.G. Unruh: Gravity wave analogues of black holes, Phys. Rev. D 66, 044019 (2002)

    Article  MathSciNet  Google Scholar 

  52. W.G. Unruh: Dumb holes: Analogues for black holes, Philos. Trans. R. Soc. A 366, 2905–2913 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  53. M. Visser: Hawking radiation without black hole entropy, Phys. Rev. Lett. 80(16), 3436 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  54. S. Weinfurtner, E.W. Tedford, M.C.J. Penrice, W.G. Unruh, G.A. Lawrence: Classical aspects of Hawking radiation verified in analogue gravity experiment. In: Analogue Gravity Phenomenology: Analogue Spacetimes and Horizons from Theory to Experiment, ed. by D. Faccio, F. Belgiorno, S. Cacciatori, V. Gorini, S. Liberati, U. Moschella (Springer, Cham 2013) pp. 167–180

    Chapter  Google Scholar 

  55. S. Weinfurtner, E.W. Tedford, M.C.J. Penrice, W.G. Unruh, G.A. Lawrence: Measurement of stimulated Hawking emission in an analogue system, Phys. Rev. Lett. 106, 021302–021305 (2011)

    Article  Google Scholar 

  56. G. Rousseaux: The basics of water waves theory for analogue gravity. In: Analogue Gravity Phenomenology: Analogue Spacetimes and Horizons from Theory to Experiment, ed. by D. Faccio, F. Belgiorno, S. Cacciatori, V. Gorini, S. Liberati, U. Moschella (Springer, Cham 2013) pp. 81–107

    Chapter  Google Scholar 

  57. M. Visser: Essential and inessential features of Hawking radiation, Int. J. Mod. Phys. D 12, 649–661 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  58. S.J. Kline: Similitude and Approximation Methods (Springer, New York 1986)

    Book  Google Scholar 

Download references

Acknowledgements

Thanks to Matt Walhout for suggesting, many years ago, that I might find William Unruh’s work on sonic analogues of black holes of interest. Later, in April 2011, I had the good fortune to attend Unruh’s lecture Measurement of Hawking Radiation in an Analog System and the discussion afterward, at the University of Pittsburgh. Thanks also to the organizers of the conference Philosophy of Scientific Experimentation III (PSX3), for financial support to present the talk this paper is based upon Experimentation on Analogs at PSX3 on October 5, 2012, at the Department of Physics, University of Colorado, Boulder. I benefitted from comments by, and discussion with, the other participants of PSX3 on the many papers related to analogy, including James Mattingly’s talk Experimental Cosmology, which also discussed experimentation on an analogue model (using Bose–Einstein condensates). Another paper on the topic of the same experiments on sonic analogues of black holes, as are discussed in this paper, was presented at the Philosophy of Science Association Biennual meeting in late 2014. As that presentation by Dardashti (and the subsequent publication of a related paper by Dardashti et al. Confirmation via Analogue Simulation: What Dumb Holes can tell us About Gravity (2015)) occurred more than 2 years after I submitted and presented Experimentation on Analoguesat PSX3 in October 2012, the talk on which my article for this volume is based, their commentary on those experiments is not discussed here.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Susan G. Sterrett .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Sterrett, S.G. (2017). Experimentation on Analogue Models. In: Magnani, L., Bertolotti, T. (eds) Springer Handbook of Model-Based Science. Springer Handbooks. Springer, Cham. https://doi.org/10.1007/978-3-319-30526-4_39

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-30526-4_39

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30525-7

  • Online ISBN: 978-3-319-30526-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics